To progress with this mission at the bar, I need to either pay money or find some metal dowels to repair the broken table. I have only just started so I am assuming there is some way for me to obtain metal dowels easily enough so that I do not need to spend money to complete this?
If you explore around the upper rooms of the bar, you will find several chests and containers that will give you more than enough metal dowels to give to the bar owner. It is also possible to craft them at a workbench if you have found enough iron but this is a waste. There are some other quests nearby that will have you exploring this bar a bit better anyway. In the process, you should more than likely find all of the items you need to complete this quest without having to pay the bar owner.